According to a PTI report, the Income Tax department has said that your PAN will become inoperative if you don't link it to Aadhaar by 31st March 2020.

The rule mentioned by the CBDT states:

Where a person, who has been allotted the permanent account number as on July 1, 2017, and is required to intimate his Aadhaar number under sub-section (2) of section 139AA, has failed to intimate the same on or before March 31, 2020, the permanent account number of such person shall become inoperative immediately after the said date for the purposes of furnishing, intimating or quoting under the Act.
Source: zeebiz

The IT department has also said that people whose PANs become inoperative will be liable to face consequences.

If you link your PAN after the deadline of 31st March 2020, your PAN will become operative from that date.

Reports suggest that over 30.75 crore PANs have already been linked to the Aadhaar till 27th January 2020. However, 17.58 crore PANs are yet to be linked.

Source: india.com

For those wondering how they can check if their Aadhaar number is linked with the PAN, here's what you can do.

Log in to www.incometaxindiaefiling.gov.in. You need to use your PAN and password to log into the portal.

Now, click on 'Profile Settings' tab and select the last option 'Link Aadhaar'. If you Aadhaar has already been linked, the screen will display the message for you.

If your PAN is not linked to Aadhaar, a form will appear. You can fill this form and you will get a confirmation message.

Alternatively, you can also link your PAN to Aadhaar number by sending an SMS to PAN service providers. You need to send the SMS to 567678 or 56161 in this format.

UIDPAN<SPACE><12 digit Aadhaar><SPACE><10 digit PAN>